Boolean Functions, equivalent truth table and gate level implementation.

A boolean function is an expression consisting for binary variables, binary operators and constants (1 or 0). The Boolean function can be used to represent a logical scenario. Sometimes the functions can be minimized to lowest possible number of variables. In this section we will discuss boolean function with an example. We will also derive a truth-table and an equivalent gate level implementation.

Boolean function example: F1 = (x + y)z’

Where F1 is a Boolean function of binary variables and binary operators. The binary variables and operators are specified below.

Binary variables = x, y and z

Binary operators = Parentheses, NOT, AND and OR

Solving or minimization of the functions are performed in a particular precedence shown below.

LTE - 4G Wireless Technology

Digital fundamentals.

Interview Questions.

Operator precedence for evaluating Boolean Expressions.

Parentheses (Highest) > NOT > AND > OR (Lowest)

Next, we will discuss the equivalent truth table for boolean function F1.

Representation of Boolean function in Truth Table.

Boolean function truth table.

The truth table above lists all the variables in function as inputs (x, y and z) and the output of function as column F1.  In order to derive a gate level implementation we will need to analyze all possible combination of inputs and corresponding output.

Next, we will discuss the equivalent gate level implementation for Function F1.


Verilog Tutorial.

LTE Tutorial.

Memory Tutorial.

The circuit is most optimized implementation of the boolean function. F1 = (x + y)z’

Boolean Function circuit.

Some more examples of Boolean Functions.

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